The Hardest Logic Paradox! | The Curry Paradox | Attic Philosophy

If this sentence is true then … we’re in trouble! The Curry paradox is like the Liar paradox, but worse! It seems to be a good proof of absolutely any sentence we like, even things we know to be false. So what's going on? Is it bad logic, or is there something else going on? Lets's take a closer look.

00:00 - Intro
00:50 - The Curry sentence
01:17 - The proof
02:12 - Does it work?
03:56 - Self-reference
04:46 - The truth predicate
05:28 - Further reading
05:53 - Wrap-up

If there’s a topic you’d like to see covered, leave me a comment below.

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#logic #philosophy #paradox

[toxications]

I don't get it, isn't the mistake made in the very first part? 1:07
The argument is that
C = C -> P
This implies
C = ( C -> P ) -> P
And recursively
C = ( ( C -> P ) -> P ) -> P
In general:
C = ( ( ... { ( ( C -> P ) -> P ) -> P } n times

But isn't it the case that because it is a self containing sentence that answer is a derivative? Therefor:
C" = C -> P
Because in order for C" to be true, both C and P are required to be true.

My apologies if my terminology is faulty and/or imprecise, I haven't studied philosophy but I'm really interested in it and I'm trying to understand this paradox.

[DustinRodriguez_]

I wasn't familiar with the paradox (or had forgotten reading about it if so), but as soon as you said "can be used to prove whatever you like" I immediately knew it was going to involve self-reference. My own approach (no idea if its proper) would be observing that the only conclusion you can come away with is what you started with. Since it is self-contained, as it were, it guarantees that it will never be possible for you to establish an argument where C is NOT assumed to be true which can prove C. Something like "This sentence has five words" can be proven without assuming its truth, as can every other valid statement. As a consequence, I think you can never reduce the statement beyond "If C, then P". Reducing it to P is misformed, because the argument presented only implies P when C is true, and on and on.

[martin.suryajaya]

Hi Mark,
How about Yablo Paradox in which the self-referentiality is construed as a (possibly) infinite hierarchy of liar sentences? And also there is the Yablurry Paradox, arguably the hardest of them all, constructed by Roy Cook as the union of Yablo and Curry Paradox. It would be very interesting if you explore these challenges in your next videos. I would like to know whether intensional logics can give a satisfactory explanation of these paradoxes (in which context of statement and context of evaluation is not necessarily identical like in classical logic or LP). Cheers

[GreenEmperor]

I thought we cannot use C -> P in a deductive proof, unless C -> P is true. I guess I am missing something here, but why can't we say that we shouldn't include C -> P in a deductive proof because it is false?

[druumondg]

Great content! Procurei por todo o youtube, por várias linguas, e este vídeo com certeza é o mais bem produzido e didático! Congrats mate :)

[tomholroyd]

If what I'm saying is true, then anything. But what I'm saying doesn't have to be true. It doesn't have to be false, either. We need to teach our children that "I don't know" is a valid truth value.

[anoukki]

Thank you very much for explaining!!

I'm currently working with your articles concerning truthmaker maximalism and negative facts. What an amazing approach in a interesting debate! I would love to see a video summarizing the challenges of truthmaker theory. (Just in case you consider video suggestions)

Thank you very much for your channel. It explains a lot to me and I enjoy your videos.

[ZMattStudio]

My consistent thought so far throughout this series is that there seems to be a conflation of the concept of truth and logical truth. We map one onto the other, but that does not mean they are the same.

[neopalm]

IF there exists a proposition C such that C <-> C->P then you can work by cases:


If C is false, C->P must be false as it is equivalent to false. However, looking at C->P, it's clear that it's true as falsehood implies anything. This leaves us with a contradiction so we can disregard this case.

If C is true, C->P must be true as it is equivalent to true. Looking at C->P, the fact that C is true indicates that P is true.

Therefore P is true.


This is actually perfectly valid logic. The only issue was the very first word. Is there really a proposition C that is equivalent to its implication of P? Well we've just done all the work to show that, by contradiction, no, whenever P is false. If P is true then any true statement will do. If P isn't true or false (i.e. there is no implication T->P or P->F) then maybe the existence of such a statement C is similarly in a middle state.

[hegelsmonster]

I'm stupid. Can someone help me? Where is the problem? The consequence of this sentence does only follow if it assume to be true. But if we just assume to be false?

[Sahilsharma-ceow]

Hello sir,
I am about to take philosophy as my UG course. I just found your channel. Can you suggest from which video or playlist shall I start?

[szefszefow]

How about semantic theory of truth? Or even simpler - I dont see any reason why shouldnt we ban self reference in the object language as a rule. Then we could allow speaking about language only in its metalanguage. I'm not sure if this solves anything, but i think this is the first condition any considerable solution Has to meet

[escher]

I think it might be interesting to investigate the iterated version of curry's paradox:
C_{n} : C_{n+1} -> P; Then we would have C_0: C_1 -> P <-> ((C_2 -> P) -> P) <-> ((((C_4 -> P) -> P) -> P) -> P) <-> -> P) -> P) -> P) -> P)-> P) -> P) -> P) -> P)
It seems like the thing about repeating a lie until it becomes true

[BelegaerTheGreat]

OMG! Given a true sentence as the consequent, the Curry statement is true. Given a false sentence as the consequent, the Curry statement is the Liar statement!


Also, suck it dialetheism.

[mattbox]

6:20 You say Modus Ponens, I say Subscribed!
(and belled.)

[Trizzer]

Dont you need some kind of axiom to make a proof? I seriously dont understand the attempt to prove anything without axioms

[mwaringmlw]

Just don't allow sets to contain themselves, and say no to infinite recursion. Stop with all this tail chasing and begging the question.

The only set that should contain itself is the null or empty set, that's how we get countable numbers, every other instance is just a shadow of that concept.

[maciej]

2:11 this is inifnite rekrusion you never proof it insdie is inifnitie end by the way C and C->P i is in loop definiable its some nonsens and question its calculable in finite time by turing machine ?

[GODemon]

Like the Liar's Paradox, it is not a logical statement and therefore should not be treated as such.

[iWinttv]

If this sentence is true, then this sentence is false.